How to find unneeded/useless vertices
Enter edit mode select one such vertex like you did in your screenshot and press Shift + G > Select Similar > Amount of connecting Edges

Exercise some caution as this will automatically select all vertex that belong only to two edges as the selected one. Be sure to inspect all the selected vertex to make sure no desirable corner vertex are mistakenly selected.

Then you can safely use X > Dissolve Vertex to delete the non-destructively